Displaying similar documents to “On the range of the derivative of a smooth mapping between Banach spaces.”

Smoothness in Banach spaces. Selected problems.

Marian Fabian, Vicente Montesinos, Václav Zizler (2006)

RACSAM

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This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and get a feeling about this area of Banach space theory. Many open problems of different level of difficulty are discussed. For...

Some properties on the closed subsets in Banach spaces

Abdelhakim Maaden, Abdelkader Stouti (2006)

Archivum Mathematicum

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It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.

Strong subdifferentiability of norms and geometry of Banach spaces

Gilles Godefroy, Vicente Montesinos, Václav Zizler (1995)

Commentationes Mathematicae Universitatis Carolinae

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The strong subdifferentiability of norms (i.eȯne-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.